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Unsteady pipe-flow using the Petrov-Galerkin finite element method

Gerber, George (2004-04)

Thesis (MScEng)--University of Stellenbosch, 2004.

Thesis

ENGLISH ABSTRACT: Presented here is an Eulerian scheme for solving the unsteady pipe-flow equations. It
is called the Characteristic Dissipative Petrov-Galerkin finite element algorithm. It is
based on Hicks and Steffler's open-channel finite element algorithm [5]. The algorithm
features a highly selective dissipative interface, which damps out spurious oscillations in
the pressure field while leaving the rest of the field almost unaffected. The dissipative
interface is obtained through upwinding of the test shape functions, which is controlled
by the characteristic directions of the flow field at a node. The algorithm can be applied
to variable grids, since the dissipative interface is locally controlled. The algorithm was
applied to waterhammer problems, which included reservoir, deadend, valve and pump
boundary conditions. Satisfactory results were obtained using a simple one-dimensional
element with linear shape functions.